← 研踪 PaperTrailarXiv:2610.41912 · v2
Decentralized Dynamic Stable Matching
首次提交 2026-10-30 23:47
版本更新 2026-11-06 15:56
雷达观测 2026-11-09 11:19
摘要
We study decentralized computing of the player-optimal stable matching under unannounced player arrivals and departures. Without a common clock, arrival/departure events information, or direct communication, players can only make individual proposals to arms and observe individual accept/reject outcomes. We measure mismatch cost --- the number of rounds in which the realized matching differs from that round's POSM, as the time horizon $T$ grows. For known preferences, we develop a deterministic polynomial-time self-calibrating protocol with mismatch cost $O(t_*+K^2\log T)$, greatly improving the existing upper-bound $O(T^{1-1/K}(\log T)^{2/K})$. $K$ is the number of arms and $t_*$ the last event time in the problem instance. Each player runs the protocol using their own local time and proposal-outcome history, without knowing~$t_*$ or $T$. More generally, configuring our protocol with a non-decreasing polynomial-time-computable function $g(t)=Ω(t)$ yields mismatch cost $O(g(t_*) + K^2 N_g(T))$, where $N_g(T)$ counts iterations of $t\mapsto t+g(t)$ below $T$. $g(t)$ reflects the protocol's convergence speed. The relationship between $g(t)$ and~$N_g(T)$ reflects the tradeoff between convergence speed and asymptotic mismatch cost. We show that any randomized protocol with convergence speed $g(t)\geq 1$ has worst-case expected cost $Ω(t_* + N_g(T))$. Thus, up to a $K^2$ factor, our protocol with $g(t)=t$ is optimal among protocols with convergence speed $O(t_*)$. For unknown preferences on both sides, each player and arm observe their own sampled utilities after being matched. We develop a decentralized learning protocol with expected mismatch cost $O(t_*+K^4Δ_{\mathrm{min}}^{-2}\log T)$, where $Δ_{\min}$ measures the preference gaps. A complementary static-setting lower-bound adapted from the literature shows that dependencies on $T$ and $Δ_{\min}$ are tight.
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v2 · 2026-11-06 15:56 · 最新观测版本
Decentralized Dynamic Stable Matching
We study decentralized computing of the player-optimal stable matching under unannounced player arrivals and departures. Without a common clock, arrival/departure events information, or direct communication, players can only make individual proposals to arms and observe individual accept/reject outcomes. We measure mismatch cost --- the number of rounds in which the realized matching differs from that round's POSM, as the time horizon $T$ grows. For known preferences, we develop a deterministic polynomial-time self-calibrating protocol with mismatch cost $O(t_*+K^2\log T)$, greatly improving the existing upper-bound $O(T^{1-1/K}(\log T)^{2/K})$. $K$ is the number of arms and $t_*$ the last event time in the problem instance. Each player runs the protocol using their own local time and proposal-outcome history, without knowing~$t_*$ or $T$. More generally, configuring our protocol with a non-decreasing polynomial-time-computable function $g(t)=Ω(t)$ yields mismatch cost $O(g(t_*) + K^2 N_g(T))$, where $N_g(T)$ counts iterations of $t\mapsto t+g(t)$ below $T$. $g(t)$ reflects the protocol's convergence speed. The relationship between $g(t)$ and~$N_g(T)$ reflects the tradeoff between convergence speed and asymptotic mismatch cost. We show that any randomized protocol with convergence speed $g(t)\geq 1$ has worst-case expected cost $Ω(t_* + N_g(T))$. Thus, up to a $K^2$ factor, our protocol with $g(t)=t$ is optimal among protocols with convergence speed $O(t_*)$. For unknown preferences on both sides, each player and arm observe their own sampled utilities after being matched. We develop a decentralized learning protocol with expected mismatch cost $O(t_*+K^4Δ_{\mathrm{min}}^{-2}\log T)$, where $Δ_{\min}$ measures the preference gaps. A complementary static-setting lower-bound adapted from the literature shows that dependencies on $T$ and $Δ_{\min}$ are tight.
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